How do i make an object visible behind a specific object?
Here is how to do it with render layers and compositor : 

Set Suzanne, Eyebrows, and hair on 3 different layers. 






Create 3 render layers with these different objects on them (here a single example, just do the same for the others) :



Then you do to the compositor, press "use node", and set up the following nodes :



Also, don't forget to set the film transparency : 



Then, select all the involved layers, and render your scene.